“There could be some changes this summer, yes,” Celtics president of operations Danny Ainge said during a news conference at their practice facility.

The Celtics need to trim their roster and made one cut Monday, waiving forward Kris Joseph, whom they also acquired in the blockbuster deal that sent Kevin Garnett, Paul Pierce, Jason Terry, and D.J. White to the Nets in exchange for a cadre of players and draft picks.

Along with Bogans, Brooks, Humphries, three first-round draft picks, and the chance to swap first-round picks in the 2017 draft, Boston also received swingman Gerald Wallace in the deal.

Wallace was absent because he had a prior commitment to attend a basketball camp.

And more changes could come as the Celtics look to clear up more roster space, especially if they have designs on signing undrafted point guard Phil Pressey, Brazilian center Vitor Faverani, or second-round draft pick Colton Iverson.

Right now, the team has 15 signed players, with one of them having a nonguaranteed deal — forward Shavlik Randolph, whose deal for about $1.1 million becomes fully guaranteed if the team doesn’t waive him by Aug. 1.

Ainge did say he believed that the players in attendance would be on the team’s roster when next season opens, but acknowledged, “We have to make some adjustments.”

For now, the only clarity, it seems, is how it came to be that Pierce and Garnett exited Boston in a massive trade that was agreed to in principle in late June.

Though Pierce and Garnett had about $40 million left on their combined contracts (about half of which was guaranteed), and though each is over the age of 35, Brooklyn ultimately made the Celtics an offer they couldn’t refuse, even if it meant the Nets would have an enormous payroll.

“Brooklyn showed a great deal of interest in putting a ‘dream team’ together — at any cost, it seemed like,” Ainge began, a reference to the spare-no-expense approach by Nets owner Mikhail Prokhorov, a Russian billionaire considered to be one of the 100 richest men on the planet.

Ainge later added, “To be able to get as many draft picks for guys at their age, it doesn’t happen very often and it wouldn’t happen if it wasn’t a team that wasn’t willing to spend a lot of tax dollars. We needed to take that opportunity.”

Ainge has said that he didn’t want these Celtics to age and decline the way the Celtics of the late 1980s did with Larry Bird, Kevin McHale, and Robert Parish all fading, in part because of injuries.

“Yes, but there’s a big difference,” Ainge said, noting that Garnett and Pierce are healthier and playing at a higher level now than those former Celtics at that late stage of their careers.

“It’s apples and oranges as to who those guys were and their longevity and durability of their careers,” he said.

“But rather than have them have a farewell tour and kind of go by the wayside, to be able to accumulate the young players that we got and the draft picks, I think as hard as it is for some fans, as hard as it is for someone like me to do, who cares a great deal about them, it was the right thing to do for the Celtics organization.”

When did it hit Ainge that this was the time to rebuild?

“It hit me when we got the offer that we got,” he said.

Had such an offer — one that Ainge said was better than any other in previous years — not arisen, they would’ve stuck with Pierce and Garnett, added pieces, and tried for another run. But, he said, this was a better option — one that would “fast forward the rebuilding process” — than having Garnett and Pierce play on a struggling team.

Ainge said it was a bonus that Pierce, Garnett, and Terry could reunite on a talent-laden team that didn’t require them to carry a heavy load, even if it is in the same division: the Atlantic.

But it was, in the end, a chance for a franchise to start over, and the same holds true for the players acquired as part of a deal that has them stepping in for a pair of Celtics legends.

“It’s going to be hard. Those two guys [are] two of the greatest players that are probably going to ever play this game,” Bogans said. “I’m not going to try to live up to what those guys did. I’m only going to do what I can do.”

Though they’re coming to a rebuilding team, Humphries said he spoke with Ainge and the message was, “We’re not tanking, we’re playing hard, you’ve got to come out here and compete, we’re trying to make it to the playoffs.”

Regarding Pierce and Garnett, Ainge said, “If it were my decision, their numbers would be hanging in the rafters some day. Their legacy has been made here in Boston and they still have basketball left in them. At the same time, we’re still going to want to beat them.”

And what does he expect when they return to TD Garden for the first time next season?

“The reaction and emotion should be a standing ovation for 10 minutes,” he said, “and to be grateful for everything they’ve given us.”

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